Experiment #3: Parallel Plate Capacitor
Student: Keith Gurr
Course: PHYS 2426L
Date: October 1, 2014
Partner: Waylon Howse
General note: This lab report is 15 pages long. This is by no means what is expected.
Most lab reports are several pages long, but nothing thing involved. This is just an
example of a student who went above & beyond.
In-depth review of the theory that
is related to the experiment. This
includes descriptions of the physics,
the equipment, definitions, equations, etc.
Statement of the objective of the laboratory experiment
Introduction
This report serves to investigate and analyze, through scientific experimentation, the
relationship between both potential difference and capacitance with the plate separation distance
In-depth review of a fixed charge parallel plate capacitor.
A capacitor (originally known as a condenser) is a passive two-terminal electrical
of the theory that
is related to the component used to store energy electrostatically in an electric field. The forms of practical
lab experiment. capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a
This includes
dielectric (i.e. insulator). The conductors can be thin films, foils or sintered beads of metal or
descriptions of
the physics, the conductive electrolyte, etc. The non-conducting dielectric acts to increase the capacitor's charge
capacity. A dielectric can be glass, ceramic, plastic film, air, vacuum, paper, mica, oxide layer
equipment,
etc. Capacitors are widely used as parts of electrical circuits in many common electrical devices.
definitions,
equations, etc. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy
in the form of an electrostatic field between its plates.
When there is a potential difference across the conductors (e.g., when a capacitor is
attached across a battery), an electric field develops across the dielectric, causing positive charge
+Q to collect on one plate and negative charge −Q to collect on the other plate. If a battery has
been attached to a capacitor for a sufficient amount of time, no current can flow through the
capacitor. However, if a time-varying voltage is applied across the leads of the capacitor, a
displacement current can flow.
An ideal capacitor is characterized by a single constant value for its capacitance.
Capacitance is expressed as the ratio of the electric charge Q on each conductor to the potential
difference V between them. The SI unit of capacitance is the farad (F), which is equal to one
coulomb per volt (1 C/V). Typical capacitance values range from about 1 pF (10−12 F) to about
1 mF (10−3 F).
The capacitance is greater when there is a narrower separation between conductors and
when the conductors have a larger surface area. In practice, the dielectric between the plates
passes a small amount of leakage current and also has an electric field strength limit, known as
the breakdown voltage. The conductors and leads introduce an undesired inductance and
resistance.
Capacitors are widely used in electronic circuits for blocking direct current while
allowing alternating current to pass. In analog filter networks, they smooth the output of power
supplies. In resonant circuits they tune radios to particular frequencies. In electric power
transmission systems, they stabilize voltage and power flow.
The simplest capacitor consists of two parallel conductive plates separated by a dielectric
(such as air) with permittivity ε. The model may also be used to make qualitative predictions for
other device geometries. The plates are considered to extend uniformly over an area A and a
charge density ±ρ = ±Q/A exists on their surface. Assuming that the width of the plates is much
greater than their separation d, the electric field near the center of the device will be uniform with
the magnitude E = ρ/ε. The voltage is defined as the line integral of the electric field between the
plates
Equations clear and
on their own lines
Solving this for C = Q/V reveals that capacitance increases with area of the plates, and
decreases as separation between plates increases.
The capacitance is therefore greatest in devices made from materials with a high
permittivity, large plate area, and small distance between plates.
A parallel plate capacitor can only store a finite amount of energy before dielectric
breakdown occurs. The capacitor's dielectric material has a dielectric strength Ud which sets the
capacitor's breakdown voltage at V = Vbd = Udd. The maximum energy that the capacitor can store
is therefore
We see that the maximum energy is a function of dielectric volume, permittivity, and
dielectric strength per distance. So increasing the plate area while decreasing the separation
between the plates while maintaining the same volume has no change on the amount of energy
the capacitor can store. Care must be taken when increasing the plate separation so that the above
assumption of the distance between plates being much smaller than the area of the plates is still
valid for these equations to be accurate. In addition, these equations assume that the electric field
is entirely concentrated in the dielectric between the plates. In reality there are fringing fields
outside the dielectric, for example between the sides of the capacitor plates, which will increase
the effective capacitance of the capacitor. This could be seen as a form of parasitic capacitance.
For some simple capacitor geometries this additional capacitance term can be calculated
analytically. It becomes negligibly small when the ratio of plate area to separation is large.
Most types of capacitor include a dielectric spacer, which increases their capacitance.
These dielectrics are most often insulators. However, low capacitance devices are available with
a vacuum between their plates, which allows extremely high voltage operation and low losses.
Variable capacitors with their plates open to the atmosphere were commonly used in radio tuning
circuits. Later designs use polymer foil dielectric between the moving and stationary plates, with
no significant air space between them.
In order to maximize the charge that a capacitor can hold the dielectric material needs to
have as high a permittivity as possible, while also having as high a breakdown voltage as
possible.
Several solid dielectrics are available, including paper, plastic, glass, mica and ceramic
materials. Paper was used extensively in older devices and offers relatively high voltage
performance. However, it is susceptible to water absorption, and has been largely replaced by
plastic film capacitors. Plastics offer better stability and ageing performance, which makes them
useful in timer circuits, although they may be limited to low operating temperatures and
frequencies. Ceramic capacitors are generally small, cheap and useful for high frequency
applications, although their capacitance varies strongly with voltage and they age poorly. Glass
and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages,
but are too expensive for most mainstream applications. Electrolytic capacitors and super
capacitors are used to store small and larger amounts of energy, respectively, ceramic capacitors
are often used in resonators, and parasitic capacitance occurs in circuits wherever the simple
conductor-insulator-conductor structure is formed unintentionally by the configuration of the
circuit layout.!
Materials and Methods
Note that this section is no longer a requirement. If you follow the lab manual
EXACTLY without deviation, you may simply write something along the lines
of “see lab manual for equipment and procedure.”
This experiment required the use of a basic variable capacitor, a DC power supply (0-8
VDC 0-5 A), a basic electrometer, a low capacitance test cable, two banana cables, and one
alligator clip.
The first portion of this experiment involved measuring and recording the radius of the
plates of the capacitor. This recorded value was used to calculate of the plate surfaces of the
capacitor. The next step was to connect the low capacitance test cable to the basic electrometer
using the BNC connection. This required the ground lead of the test cable to be connected to the
movable plate and the other lead to be connected to the fixed plate of the capacitor. The next step
was to use the two banana cables to connect the ground of the DC power supply to the
electrometer and the positive terminal to the alligator clip. The alligator clip was then connected
to the fixed plate of the capacitor. The next step was to turn on the DC power supply and adjust
the voltage reading until a reading of 30 V was displayed on the electrometer. The positive
alligator clip lead was then removed from the fixed plate of the capacitor. The final step of this
portion of the experiment was to the set the plate separation of the capacitor to 10 cm. This
distance value along with corresponding potential difference value was then recorded on the data
sheet.
The second portion of this experiment involved repeating all the steps performed in the
first portion using gradually decreased plate separation distances. For plate separation distances
greater than 5 cm, the separation distance was lowered in 1 cm increments. For plate separation
distances less than 5 cm, the separation distance was lowered in 0.5 cm increments. Each of
these decreased plate separation distances and the corresponding measured potential difference
value was recorded on the data sheet. As a final step in this portion of the experiment, the
amount of capacitance for each of the recorded separation distances including the initial 10 cm
was calculated and recorded on the data sheet.
The third portion of this experiment began by conducting a second trial of the entire
experiment. This involved repeating all the steps performed in the first and second portions and
recording all the relevant results obtained on the data sheet. Once this was completed, the DC
power supply was turned off and the entire equipment set up was dismantled to pre-experiment
configuration.
The final portion of this experiment involved using the spreadsheet program Excel to
generate two graphical plots of the recorded data. The first of these plots graphically compared
the potential difference values to the corresponding plate separation values while the second of
these plots graphically compared the calculated capacitance values to the corresponding plate
separation values. Both of the two plots contained the data obtained from the first and second
trials of the experiment. A line of best fit was also incorporated into each plot and for each of the
two trials.
Tables are often introduced with a few sentences.
Results
Table 1 contains the recorded measurement of the radius of the parallel plates of the basic
variable capacitor for Trial 1. It also contains the calculated measurement for the area of the
same parallel plates. The formula used to calculate the area is as follows:
A = πr2
Using the above formula, the value for the area of the parallel plates was calculated as
follows:
r = 8.90 x 10-2 m
r = 8.90 cm
A = (π) (8.90 x 10-2 m)2
A = (π) (7.92 x 10-3 m2)
A = 2.49 x 10-2 m2
A= 2.49 x 102 cm2
Parallel Plates
Table 1 – Trial 1
Radius (cm)
8.90 cm
Area (cm2)
2.49 x 102 cm2
Table 1: Radius and Area of the Parallel Plates of the Capacitor for Trial 1
table footnotes are sometimes
useful, but not necessary
Table 2 contains the recorded separation distances in meters and corresponding recorded
potential difference (voltage) values in volts for Trial 1 of this experiment. It also contains the
corresponding calculated capacitance values in farads for Trial 1 of the experiment. The formula
used to calculate the capacitance is as follows:
C = (ε0)(A/d)
Using the above formula, the value for the capacitance for each of the measured plate
separation distances was calculated as follows:
ε0 = 8.854 x 10-12 F/m
A = 2.49 x 10-2 m2
d = plate separation distance
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (1.00 x 10-2 m))
C = (8.854 x 10-12 F/m) (2.49 m)
C = 2.20 x 10-11 F
C = 2.20 x 10-5 µF
Sample calculations are required.
Show at least one sample calculation
for every formula used. Show all steps.
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.90 x 10-2 m))
C = (8.854 x 10-12 F/m) (2.76 m)
C = 2.44 x 10-11 F
C = 2.44 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.80 x 10-2 m))
C = (8.854 x 10-12 F/m) (3.11 m)
C = 2.75 x 10-11 F
C = 2.75 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.70 x 10-2 m))
C = (8.854 x 10-12 F/m) (3.55 m)
C = 3.14 x 10-11 F
C = 3.14x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.60 x 10-2 m))
C = (8.854 x 10-12 F/m) (4.14 m)
C = 3.67 x 10-11 F
C = 3.67 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.50 x 10-2 m))
C = (8.854 x 10-12 F/m) (4.97 m)
C = 4.40 x 10-11 F
C = 4.40 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.45 x 10-2 m))
C = (8.854 x 10-12 F/m) (5.52 m)
C = 4.89 x 10-11 F
C = 4.89 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.40 x 10-2 m))
C = (8.854 x 10-12 F/m) (6.21 m)
C = 5.50 x 10-11 F
C = 5.50 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.35 x 10-2 m))
C = (8.854 x 10-12 F/m) (7.10 m)
C = 6.29 x 10-11 F
C = 6.29 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.30 x 10-2 m))
C = (8.854 x 10-12 F/m) (8.28 m)
C = 7.33 x 10-11 F
C = 7.33 x 10-5 µF
* NOTE: this student does EVERY calculation.
This is borderline crazy and is not required.
However, it may be useful to have everything
done in one place!
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.25 x 10-2 m))
C = (8.854 x 10-12 F/m) (9.94 m)
C = 8.80 x 10-11 F
C = 8.80 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.20 x 10-2 m))
C = (8.854 x 10-12 F/m) (12.43 m)
C = 11.00 x 10-11 F
C = 11.00 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.15 x 10-2 m))
C = (8.854 x 10-12 F/m) (16.57 m)
C = 14.67 x 10-11 F
C = 14.67 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.10 x 10-2 m))
C = (8.854 x 10-12 F/m) (24.85 m)
C = 22.00 x 10-11 F
C = 22.00 x 10-5 µF
Tables are very neat. Each table has a title.
Column headings are bolded and include
the units in parentheses. Note that since he
included the units in the column headings,
he didn’t need to put them after every single
value within the table.
C = (8.854 x 10-12 F/m) ((2.49 x 10-2 m2) / (0.05 x 10-2 m))
C = (8.854 x 10-12 F/m) (49.70 m)
C = 44.00 x 10-11 F
C = 44.00 x 10-5 µF
Potential Difference / Voltage (V)
15.50 V
15.00 V
14.00 V
13.50 V
12.50 V
12.00 V
11.00 V
10.50 V
9.50 V
9.00 V
8.00 V
7.50 V
7.00 V
6.00 V
5.50 V
Table 2 – Trial 1
Separation Distance (cm)
10.0 cm
9.0 cm
8.0 cm
7.0 cm
6.0 cm
5.0 cm
4.5 cm
4.0 cm
3.5 cm
3.0 cm
2.5 cm
2.0 cm
1.5 cm
1.0 cm
0.5 cm
Capacitance (µF)
2.20 x 10-5 µF
2.44 x 10-5 µF
2.75 x 10-5 µF
3.14 x 10-5 µF
3.67 x 10-5 µF
4.40 x 10-5 µF
4.89 x 10-5 µF
5.50 x 10-5 µF
6.29 x 10-5 µF
7.33 x 10-5 µF
8.80 x 10-5 µF
11.00 x 10-5 µF
14.67 x 10-5 µF
22.00 x 10-5 µF
44.00 x 10-5 µF
Table 2: Potential Difference, Separation Distance, and Capacitance Values for Trial 1
Table 3 contains the recorded measurement of the radius of the parallel plates of the basic
variable capacitor for Trial 2. It also contains the calculated measurement for the area of the
same parallel plates. The formula used to calculate the area is as follows:
A = πr2
Using the above formula, the value for the area of the parallel plates was calculated as
follows:
r = 8.70 x 10-2 m
r = 8.70 cm
A = (π) (8.70 x 10-2 m)2
A = (π) (7.57 x 10-3 m2)
A = 2.38 x 10-2 m2
A= 2.38 x 102 cm2
Parallel Plates
Table 3 – Trial 2
Radius (cm)
8.70 cm
Area (cm2)
2.38 x 102 cm2
Table 3: Radius and Area of the Parallel Plates of the Capacitor for Trial 2
Table 4 contains the recorded separation distances in meters and corresponding recorded
potential difference (voltage) values in volts for Trial 2 of this experiment. It also contains the
corresponding calculated capacitance values in farads for Trial 2 of the experiment. The formula
used to calculate the capacitance is as follows:
C = (ε0)(A/d)
Using the above formula, the value for the capacitance for each of the measured plate
separation distances was calculated as follows:
ε0 = 8.854 x 10-12 F/m
A = 2.38 x 10-2 m2
d = plate separation distance
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (1.00 x 10-2 m))
C = (8.854 x 10-12 F/m) (2.38 m)
C = 2.10 x 10-11 F
C = 2.10 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.90 x 10-2 m))
C = (8.854 x 10-12 F/m) (2.64 m)
C = 2.34 x 10-11 F
C = 2.34 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.80 x 10-2 m))
C = (8.854 x 10-12 F/m) (2.97 m)
C = 2.63 x 10-11 F
C = 2.63 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.70 x 10-2 m))
C = (8.854 x 10-12 F/m) (3.40 m)
C = 3.01 x 10-11 F
C = 3.01 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.60 x 10-2 m))
C = (8.854 x 10-12 F/m) (3.96 m)
C = 3.51 x 10-11 F
C = 3.51 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.50 x 10-2 m))
C = (8.854 x 10-12 F/m) (4.75 m)
C = 4.21 x 10-11 F
C = 4.21 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.45 x 10-2 m))
C = (8.854 x 10-12 F/m) (5.28 m)
C = 4.68 x 10-11 F
C = 4.68 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.40 x 10-2 m))
C = (8.854 x 10-12 F/m) (5.94 m)
C = 5.26 x 10-11 F
C = 5.26 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.35 x 10-2 m))
C = (8.854 x 10-12 F/m) (6.79 m)
C = 6.01 x 10-11 F
C = 6.01 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.30 x 10-2 m))
C = (8.854 x 10-12 F/m) (7.92 m)
C = 7.02 x 10-11 F
C = 7.02 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.25 x 10-2 m))
C = (8.854 x 10-12 F/m) (9.51 m)
C = 8.42 x 10-11 F
C = 8.42 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.20 x 10-2 m))
C = (8.854 x 10-12 F/m) (11.89 m)
C = 10.52 x 10-11 F
C = 10.52 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.15 x 10-2 m))
C = (8.854 x 10-12 F/m) (15.85 m)
C = 14.03 x 10-11 F
C = 14.03 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.10 x 10-2 m))
C = (8.854 x 10-12 F/m) (23.77 m)
C = 21.05 x 10-11 F
C = 21.05 x 10-5 µF
C = (8.854 x 10-12 F/m) ((2.38 x 10-2 m2) / (0.05 x 10-2 m))
C = (8.854 x 10-12 F/m) (47.54 m)
C = 42.09 x 10-11 F
C = 42.09 x 10-5 µF
Potential Difference / Voltage (V)
15.75 V
15.00 V
14.25 V
13.50 V
12.75 V
12.00 V
11.25 V
10.50 V
9.75 V
9.00 V
8.25 V
7.50 V
6.75 V
6.00 V
5.25 V
Table 4 – Trial 2
Separation Distance (cm)
10.0 cm
9.0 cm
8.0 cm
7.0 cm
6.0 cm
5.0 cm
4.5 cm
4.0 cm
3.5 cm
3.0 cm
2.5 cm
2.0 cm
1.5 cm
1.0 cm
0.5 cm
Capacitance (µF)
2.10 x 10-5 µF
2.34 x 10-5 µF
2.63 x 10-5 µF
3.01 x 10-5 µF
3.51 x 10-5 µF
4.21 x 10-5 µF
4.68 x 10-5 µF
5.26 x 10-5 µF
6.01 x 10-5 µF
7.02 x 10-5 µF
8.42 x 10-5 µF
10.52 x 10-5 µF
14.03 x 10-5 µF
21.05 x 10-5 µF
42.09 x 10-5 µF
Table 4: Potential Difference, Separation Distance, and Capacitance Values for Trial 2
Graph 1 contains the plot of the potential difference (voltage) values versus the
corresponding plate separation distance values for trial 1 and trial 2.
Poten&al)Difference)/)Voltage)(V))
Poten&al)Difference)/)Voltage)vs.)
Plate)Separa&on)Distance)
18!
16!
14!
12!
10!
8!
6!
4!
2!
0!
Gorgeous graphs that
include chart titles and
axes titles.
Trial!1!
Trial!2!
10! 9! 8! 7! 6! 5! 4.5! 4! 3.5! 3! 2.5! 2! 1.5! 1! 0.5!
Separa&on)Distance)(cm))
You only need to
include a legend if
you are plotting two
or more sets of data
on the same graph.
Often, we will only be
plotting one set of
data, so this may be
be deleted in those
cases.
Graph 1: Potential Difference / Voltage vs. Plate Separation Distance for Trial 1 and Trial 2
Graph 2 contains the plot of the capacitance values versus the corresponding plate
separation distance values for trial 1 and trial 2.
Capacitance)(1)x)10>6)µF))
Capacitance)vs.)Plate)Separa&on)
Distance)
50!
45!
40!
35!
30!
25!
20!
15!
10!
5!
0!
Trial!1!
Trial!2!
10! 9! 8! 7! 6! 5! 4.5! 4! 3.5! 3! 2.5! 2! 1.5! 1! 0.5!
Separa&on)Distance)(cm))
Graph 2: Capacitance vs. Plate Separation Distance for Trial 1 and Trial 2
Discussion
The results of this experiment as shown in Tables 1 through 4 and in Graphs 1 and 2
reveal the parallel plate radius, plate separation distances, and potential difference (voltage)
A quick summary
of the results and
values measured and recorded for both Trial 1 and Trial 2 of this experiment. These
measurements can be used to calculate additional measurements related to the experiment. The what you did
radius of the parallel plates, for example allowed for the area of the parallel plates to be
determined. The standard formula for the area of a circle was used due to the circular shape of
the parallel plates. This calculated area, combined with the recorded measurements for the plate
separation distances , was then used to determine each of the corresponding capacitance values.
In-depth
The formula used to calculate capacitance can be expressed as a ratio of the area of the parallel
analysis of
plates divided by the separation distance with the result multiplied by what is known as the
what the data
vacuum permittivity constant.
shows.
The results for both Trial 1 and Trial 2, as evident both numerically in Tables 2 and 4 and
graphically in Graph 1 show that a decrease in plate separation causes the potential difference or
voltage to also decrease. Graph 1 clearly shows that this decrease in potential difference is nearly
proportional to the decrease in plate separation distance allowing for error in the experiment. The Back up your
analysis by
results of Trial 1 for example, show that at a separation distance of 10.0 cm, the voltage was
15.50 V. When the separation distance dropped down to only 0.5 cm, the voltage had decreased using an
to 5.5 V. The same pattern was observed in Trial 2. The results of Trial 2 for example, show that example
directly from
at a separation distance of 10.0 cm, the voltage was 15.75 V. When the separation distance
your own data
dropped down to only 0.5 cm, the voltage had decreased to 5.25 V. This outcome indicates and
confirms the previous conclusion that a decrease in plate separation distance results in a decrease
in potential difference or voltage.
A contrasting pattern occurs when the results for the plate separation distances and
corresponding capacitance values are compared. The results for both Trial 1 and Trial 2, as
evident both numerically in Tables 2 and 4 and graphically in Graph 2 show that a decrease in
plate separation causes capacitance to increase. Graph 2 clearly shows that this decrease in
potential difference is consistent with the increase in capacitance with the greatest increases
occurring at the smaller plate separation distances. This pattern occurred in both Trial 1 and Trial
2 of the experiment. The results of Trial 1 for example, show that at a separation distance of 10.0
cm, the capacitance was 2.20 x 10-5 µF. When the separation distance dropped down to only 0.5
cm, the capacitance had increased to 44.00 x 10-5 µF. The same pattern was observed in Trial 2.
The results of Trial 2 for example, show that at a separation distance of 10.0 cm, the capacitance
was 2.10 x 10-5 µF. When the separation distance dropped down to only 0.5 cm, the capacitance
had increased to 42.09 x 10-5 µF. This outcome indicates and confirms the previous conclusion
that a decrease in plate separation distance results in an increase in capacitance.
The relationship that exists between plate separation distance and potential difference and
between plate separation distance and capacitance can be further understood through an example.
Assume a parallel plate capacitor consists of two circular plates each of radius 40 cm separated
by 0.3 cm. The area of the plates would be calculated as follows:
A = (π) (r)2
A = (π) (4.0 x 10-1 m)2
A = (π) (1.6 x 10-1 m2)
A = 5.0 x 10-1 m2 ≈ 50 cm
This was a post-lab question. Notice how he integrates
the problem directly into his discussion. This creates a nicely
flowing document and looks great. He doesn’t just simply create
a numbered list and write each question with their answers.
You must show your work for any computational problems given!
It is now possible to calculate the capacitance that is present given that the area and plate
separation distance are known. The capacitance would be calculated as follows:
A = area of plate
d = plate separation distance
ε0 = vacuum permittivity constant
C = capacitance
C = (ε0)(A/d)
C = (8.854 x 10-12 F/m) ((5.03 x 10-1 m2) / (3.00 x 10-3 m))
C = (8.854 x 10-12 F/m) (1.67 x 103 m)
C = 1.48 x 10-9 F
C = 1.48 x 10-3 µF
As a further extension of this example, the relationship between capacitance, charge, and
potential difference can be examined. Assume that the capacitor is required to hold a charge of
3µC. The capacitance is known from the calculation above. With these two numerical values, it
is possible to determine the potential difference that must be applied. The potential difference
would be calculated as follows:
C = capacitance
Q = charge
V = potential difference
C=Q/V
CV = Q
V=Q/C
V = (3 x 10-6 C) / (1.48 x 10-9 F)
V = 2.03 x 103 C/F
Very important: A discussion of errors! Note what caused or
might have caused any errors. Mention how it may have
influenced your results. How might you be able to reduce
and/or fix these errors? Do your best to analyze everything
that was used (equipment and procedure methods) and
develop logical arguments/explanations.
The results of this experiment, while effectively conveying the relationship that exists
between the plate separation distance and potential difference as well as capacitance, are prone to
sources of error present in the experiment.
One of the key sources of error relates to the equipment used. The first of this equipment
is the electrometer. This device proved to be extremely sensitive to any sort of movement or
disturbance in the air surrounding it. This sensitivity created a high possibility for potential
difference measurements that were not accurate as a result of nearby air movement or
interference from other electronic devices. This possibility was detected and an effort was made
to isolate the electrometer as much as possible however the sensitivity of the device remained.
As a step towards reducing error, future attempts to conduct the experiment could involve
ensuring that the electrometer is kept at a sufficient distance from other electronic devices as
well as lab participants and other sources of air movement.
A second piece of equipment used was the DC power supply. This device could have
been a source of error if it was not functioning correctly and consequently giving false readings.
A faulty power supply could have caused the electrometer to have received either an excessive or
insufficient amount of voltage despite a voltage reading of 30 V being displayed on the
electrometer. This possibility could have created inaccurate or invalid potential difference
readings. In order to reduce the chances of such error, the DC power supply could be pretested
for proper functionality prior to conducting the experiment.
A final source of error present in this experiment is that generated by participants in the
lab. While every effort was made to ensure that all data values were correctly measured and
recorded, it is likely that a certain degree of human error likely impacted the recorded values. To
reduce the presence of this type of error when conducting this experiment, data values could be
measured and verified by more than one lab participant prior to the values being recorded. This
would ensure that any discrepancies in the data would be addressed and resolved as necessary.
Works Cited
“Capacitor.” Wikepedia. Wikepedia Foundation Inc. 29 September 2014. 29 September 2014.
http://en.wikipedia.org/wiki/Capacitor
A works cited page is REQUIRED if you pull ANY information or images
from other sources (i.e. books, internet, etc.). Do your best to conform to
the current MLA format. I give a link to a website to help you with writing
a proper works cited page. If your writing is beyond your level, I will likely
notice and will search what you wrote to make sure you didn’t copy (especially
without citing your source). If it becomes a problem, you could face some nasty
drops in your grades and, if it is a constant issue, I may have to let an administrator
know…please dont make me do that. It isn't that hard to write in your own words!